Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation

37 Pages Posted: 13 Jan 2012 Last revised: 26 Feb 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Michel Lubrano

Ecole des Hautes Etudes en Sciences Sociales (EHESS)

Date Written: March 8, 2010

Abstract

Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution that we derive. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with a Student t(ν) kernel which includes the Gaussian as a special case, the CV criterion becomes asymptotically equivalent to a simple polynomial. This leads to optimal-bandwidth solutions that dominate the usual CV methods, definitely in terms of simplicity and speed of calculation, but also often in terms of integrated squared error because of the robustness of our asymptotic solution, hence also alleviating the notorious sample variability of CV. We present simulations to illustrate these features and to give practical guidance on the choice of ν.

Suggested Citation

Abadir, Karim M. and Lubrano, Michel, Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation (March 8, 2010). Available at SSRN: https://ssrn.com/abstract=1984825 or http://dx.doi.org/10.2139/ssrn.1984825

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Michel Lubrano

Ecole des Hautes Etudes en Sciences Sociales (EHESS) ( email )

Greqam, Vieille Charité
2 rue de la Charité
13002 Marseille
France

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